Average of cubes of first n natural numbers
The average of cubes of the first n natural numbers is the sum of the cubes of the first n natural numbers, divided by n.
Using the formula for the sum of cubes of the first n natural numbers, which is (n*(n+1)/2)^2, we can simplify the expression as follows:
average = (1/n) * (1³ + 2³ + 3³ + ... + n³)
average = (1/n) * [n²*(n+1)² / 4] (using the formula for the sum of cubes)
average = (n*(n+1)²) / 4
Therefore, we can calculate the average of cubes of the first n natural numbers using the formula (n*(n+1)²) / 4.
Program Solution
// C Program
// Average of cubes of first n natural numbers
#include <stdio.h>
void findAverageOfCube(int n)
{
if (n <= 0)
{
return;
}
// Calculate cube of n natural number
// Formula = (n×(n+1)²) / 4
double average = (n * (n + 1) * (n + 1)) / 4.0;
// Display calculated result
printf("\n %lf", average);
}
int main()
{
int n = 6;
/*
n = 6
---------------------------
1³ + 2³ + 3³ + 4³ + 5³ + 6³ = (440)
----------------------------
440
-- = 73.5
6
*/
findAverageOfCube(n);
return 0;
}Output
73.500000// Java program for
// Average of cubes of first n natural numbers
public class Average
{
public void findAverageOfCube(int n)
{
if (n <= 0)
{
return;
}
// Calculate cube of n natural number
// Formula = (n×(n+1)²) / 4
double average = (n * (n + 1) * (n + 1)) / 4.0;
// Display calculated result
System.out.print("\n " + average);
}
public static void main(String[] args)
{
Average task = new Average();
int n = 6;
/*
n = 6
---------------------------
1³ + 2³ + 3³ + 4³ + 5³ + 6³ = (440)
----------------------------
440
-- = 73.5
6
*/
task.findAverageOfCube(n);
}
}Output
73.5// Include header file
#include <iostream>
using namespace std;
// C++ program for
// Average of cubes of first n natural numbers
class Average
{
public: void findAverageOfCube(int n)
{
if (n <= 0)
{
return;
}
// Calculate cube of n natural number
// Formula = (n×(n+1)²) / 4
double average = (n *(n + 1) *(n + 1)) / 4.0;
// Display calculated result
cout << "\n " << average;
}
};
int main()
{
Average *task = new Average();
int n = 6;
/*
n = 6
---------------------------
1³ + 2³ + 3³ + 4³ + 5³ + 6³ = (440)
----------------------------
440
-- = 73.5
6
*/
task->findAverageOfCube(n);
return 0;
}Output
73.5// Include namespace system
using System;
// Csharp program for
// Average of cubes of first n natural numbers
public class Average
{
public void findAverageOfCube(int n)
{
if (n <= 0)
{
return;
}
// Calculate cube of n natural number
// Formula = (n×(n+1)²) / 4
double average = (n * (n + 1) * (n + 1)) / 4.0;
// Display calculated result
Console.Write("\n " + average);
}
public static void Main(String[] args)
{
Average task = new Average();
int n = 6;
/*
n = 6
---------------------------
1³ + 2³ + 3³ + 4³ + 5³ + 6³ = (440)
----------------------------
440
-- = 73.5
6
*/
task.findAverageOfCube(n);
}
}Output
73.5package main
import "fmt"
// Go program for
// Average of cubes of first n natural numbers
type Average struct {}
func getAverage() * Average {
var me *Average = &Average {}
return me
}
func(this Average) findAverageOfCube(n int) {
if n <= 0 {
return
}
// Calculate cube of n natural number
// Formula = (n×(n+1)²) / 4
var average float64 = float64(n * (n + 1) * (n + 1)) / 4.0
// Display calculated result
fmt.Print("\n ", average)
}
func main() {
var task * Average = getAverage()
var n int = 6
/*
n = 6
---------------------------
1³ + 2³ + 3³ + 4³ + 5³ + 6³ = (440)
----------------------------
440
-- = 73.5
6
*/
task.findAverageOfCube(n)
}Output
73.5<?php
// Php program for
// Average of cubes of first n natural numbers
class Average
{
public function findAverageOfCube($n)
{
if ($n <= 0)
{
return;
}
// Calculate cube of n natural number
// Formula = (n×(n+1)²) / 4
$average = ($n * ($n + 1) * ($n + 1)) / 4.0;
// Display calculated result
echo("\n ".$average);
}
}
function main()
{
$task = new Average();
$n = 6;
/*
n = 6
---------------------------
1³ + 2³ + 3³ + 4³ + 5³ + 6³ = (440)
----------------------------
440
-- = 73.5
6
*/
$task->findAverageOfCube($n);
}
main();Output
73.5// Node JS program for
// Average of cubes of first n natural numbers
class Average
{
findAverageOfCube(n)
{
if (n <= 0)
{
return;
}
// Calculate cube of n natural number
// Formula = (n×(n+1)²) / 4
var average = (n * (n + 1) * (n + 1)) / 4.0;
// Display calculated result
process.stdout.write("\n " + average);
}
}
function main()
{
var task = new Average();
var n = 6;
/*
n = 6
---------------------------
1³ + 2³ + 3³ + 4³ + 5³ + 6³ = (440)
----------------------------
440
-- = 73.5
6
*/
task.findAverageOfCube(n);
}
main();Output
73.5# Python 3 program for
# Average of cubes of first n natural numbers
class Average :
def findAverageOfCube(self, n) :
if (n <= 0) :
return
# Calculate cube of n natural number
# Formula = (n×(n+1)²) / 4
average = (n * (n + 1) * (n + 1)) / 4.0
# Display calculated result
print("\n ", average, end = "")
def main() :
task = Average()
n = 6
# n = 6
# ---------------------------
# 1³ + 2³ + 3³ + 4³ + 5³ + 6³ = (440)
# ----------------------------
# 440
# -- = 73.5
# 6
task.findAverageOfCube(n)
if __name__ == "__main__": main()Output
73.5# Ruby program for
# Average of cubes of first n natural numbers
class Average
def findAverageOfCube(n)
if (n <= 0)
return
end
# Calculate cube of n natural number
# Formula = (n×(n+1)²) / 4
average = (n * (n + 1) * (n + 1)) / 4.0
# Display calculated result
print("\n ", average)
end
end
def main()
task = Average.new()
n = 6
# n = 6
# ---------------------------
# 1³ + 2³ + 3³ + 4³ + 5³ + 6³ = (440)
# ----------------------------
# 440
# -- = 73.5
# 6
task.findAverageOfCube(n)
end
main()Output
73.5// Scala program for
// Average of cubes of first n natural numbers
class Average()
{
def findAverageOfCube(n: Int): Unit = {
if (n <= 0)
{
return;
}
// Calculate cube of n natural number
// Formula = (n×(n+1)²) / 4
var average: Double = (n * (n + 1) * (n + 1)) / 4.0;
// Display calculated result
print("\n " + average);
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: Average = new Average();
var n: Int = 6;
/*
n = 6
---------------------------
1³ + 2³ + 3³ + 4³ + 5³ + 6³ = (440)
----------------------------
440
-- = 73.5
6
*/
task.findAverageOfCube(n);
}
}Output
73.5// Swift 4 program for
// Average of cubes of first n natural numbers
class Average
{
func findAverageOfCube(_ n: Int)
{
if (n <= 0)
{
return;
}
// Calculate cube of n natural number
// Formula = (n×(n+1)²) / 4
let average: Double = Double(n * (n + 1) * (n + 1)) / 4.0;
// Display calculated result
print("\n ", average, terminator: "");
}
}
func main()
{
let task: Average = Average();
let n: Int = 6;
/*
n = 6
---------------------------
1³ + 2³ + 3³ + 4³ + 5³ + 6³ = (440)
----------------------------
440
-- = 73.5
6
*/
task.findAverageOfCube(n);
}
main();Output
73.5// Kotlin program for
// Average of cubes of first n natural numbers
class Average
{
fun findAverageOfCube(n: Int): Unit
{
if (n <= 0)
{
return;
}
// Calculate cube of n natural number
// Formula = (n×(n+1)²) / 4
val average: Double = (n * (n + 1) * (n + 1)) / 4.0;
// Display calculated result
print("\n " + average);
}
}
fun main(args: Array < String > ): Unit
{
val task: Average = Average();
val n: Int = 6;
/*
n = 6
---------------------------
1³ + 2³ + 3³ + 4³ + 5³ + 6³ = (440)
----------------------------
440
-- = 73.5
6
*/
task.findAverageOfCube(n);
}Output
73.5
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